the indicial roots of the singularity. xảy" + (1.5x+x2)y −0.5y=0 a. (r+1)(r-2) = 0 b. (r+ 1)(2r-1)=0 c. (r-1)(2r-1) = 0 d. (r-1)(2r+ 1) = 0 a Ob d
the indicial roots of the singularity. xảy" + (1.5x+x2)y −0.5y=0 a. (r+1)(r-2) = 0 b. (r+ 1)(2r-1)=0 c. (r-1)(2r-1) = 0 d. (r-1)(2r+ 1) = 0 a Ob d
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Indicial Roots of a Differential Equation
**Problem Statement:**
The point \( x = 0 \) is a regular singular point of the given differential equation. Find the equation for the indicial roots of the singularity.
\[ x^2y'' + (1.5x + x^2)y' - 0.5y = 0 \]
Given options:
a. \( (r + 1)(r - 2) = 0 \)
b. \( (r + 1)(2r - 1) = 0 \)
c. \( (r - 1)(2r - 1) = 0 \)
d. \( (r - 1)(2r + 1) = 0 \)
**Choices:**
- ○ a
- ○ b
- ○ c
- ○ d
**Graph/Diagram Explanation:**
No graphs or diagrams are included in this part of the problem. The task involves algebraic manipulation of the differential equation to determine the correct indicial equation and its roots.
For a differential equation problem involving indicial roots, standard procedures generally require forming a characteristic equation by substituting a trial solution and equating the coefficients to find the roots.
**To Proceed:**
You might start by transforming the differential equation using the Frobenius method and then applying the corresponding initial conditions to derive the indicial equation. Once derived, compare the characteristic polynomial to the options provided to determine the correct indicial roots.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d2af6b8-35d3-4327-94c1-a05ff77beaf0%2F55cde624-a032-463c-99fe-b6f09a994153%2Fza2lto_processed.png&w=3840&q=75)
Transcribed Image Text:### Indicial Roots of a Differential Equation
**Problem Statement:**
The point \( x = 0 \) is a regular singular point of the given differential equation. Find the equation for the indicial roots of the singularity.
\[ x^2y'' + (1.5x + x^2)y' - 0.5y = 0 \]
Given options:
a. \( (r + 1)(r - 2) = 0 \)
b. \( (r + 1)(2r - 1) = 0 \)
c. \( (r - 1)(2r - 1) = 0 \)
d. \( (r - 1)(2r + 1) = 0 \)
**Choices:**
- ○ a
- ○ b
- ○ c
- ○ d
**Graph/Diagram Explanation:**
No graphs or diagrams are included in this part of the problem. The task involves algebraic manipulation of the differential equation to determine the correct indicial equation and its roots.
For a differential equation problem involving indicial roots, standard procedures generally require forming a characteristic equation by substituting a trial solution and equating the coefficients to find the roots.
**To Proceed:**
You might start by transforming the differential equation using the Frobenius method and then applying the corresponding initial conditions to derive the indicial equation. Once derived, compare the characteristic polynomial to the options provided to determine the correct indicial roots.
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